Circuit Elements Required for Neural Systems - Brain Theory from a Circuits and Systems Perspective - page 35

The parameter β ¼ 86.66 is chosen so that at 2.5 ms the voltage has decreased to

90 mV. The current then drifts to a rest voltage 70 mV. An interesting parameter

is the time required for the model to go from Δ ¼ +40 to 55 mV (Fig. 3.2 ):

95
β

t Δ ¼ 1 þ ms (3.3)

At 55 mV or less a membrane is no longer triggered, so t Δ defines a pulse width.

This simple model ignores membrane conductance.
Note for future reference that as beta decreases, the time for which voltage
remains above

55 mV goes up geometrically! If β ¼ 0.1 the time involved is

about 1 s.
Another way to look at a pulse is that a neural membranes may be thought of as
following a hysteresis loop as in Fig. 3.3 . E refers to electric field and D to a
displacement within each affected molecule. Once charging stops at roughly
+40 mV there is a steady discharge down past

90 mV
which snaps the molecules into their original condition. Then voltage drifts to a rest
level, about

70 mV and to about

70 mV. The hysteresis loop is a common property of materials and
portrays membranes from a different point of view.

Delay Elements

Delay in dendrites is very roughly 15 ms/cm. Signal delay is determined by the
length of the path and also the membrane capacitance of the path, and such current-
charging parameters as the density of conductive pores (or ion channels) in an
unmyelinated neural conductor and also by local ionic concentrations. Inhibitory

Short term memory durations

10 4

10 3

10 2

10 1

10 0

10 -2 10 -1 10 0 10 1 10 2

Fig. 3.2 Time (ms) to move
from +40 to

Beta

55 mV versus β